8.F.2: Compare Linear Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope is negative.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope means that as x increases, y also increases, resulting in an upward line. A negative slope means that as x increases, y decreases, resulting in a downward line.

Front

How can you compare two linear functions?

Back

You can compare two linear functions by examining their slopes and y-intercepts. The function with the greater slope increases faster.

Front

What is a function's domain?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is a function's range?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for two linear functions to be parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two linear functions to be perpendicular?

Back

Two linear functions are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.